DISTRIBUTED GENERATORS AND
VOLTAGE STABILITY
Konstantin Turitsyn & Hung Nguyen
Mechanical Engineering Department
Massachusetts Institute of Technology
turitsyn@mit.edu; hunghtd@mit.edu
02/03/14
MOTIVATION
•  Distributed generation (PV, Wind, Gas):
–  Increased reliability
–  Unconventional operating states
•  Distributed control of active and reactive power:
–  New generation of OPF-type algorithms
–  Mostly static analysis, implicit assumption of static and
transient stability
Konstantin Turitsyn & Hung Nguyen, 02/03/14
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OUTLINE
•  Distributed generators’ effects on distributed
networks
•  System equations and dynamic load modeling
•  Dynamic stability criterion based on static solutions
•  Dynamic simulations
–  Trapped at the lower branch
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Power reversal creates new regimes
•  Multiple power flow solutions
–  High voltage solutions complies
with voltage standards
•  New protection and control
systems are required
unit: p.u.
+ : consuming
- : injecting
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Power reversal and load dynamics affect the
stability properties
•  Unstable equilibrium may appear
on the upper branch of the nose
curve; whereas, new stable ones
may exist at the lower branch.
•  The diversity of load dynamics
with the presence of DGs may
jeopardize the voltage security of
the system.
Stable
Unstable
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DAE of the system
x: states
y: algebraic variables
p: parameters
•  Slow dynamics vs. fast dynamics
•  Algebraic equations
–  Load flow equation vs. Kirchhoff laws: typically,
the algebraic equations are considered as power
flow equations.
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Dynamic load modeling
•  Various electric loads and regulators are
designed to consume a fixed level of powers in
order to achieve the desired performance.
y = g +jb
–  Voltage regulators
g
–  Thermostats …
•  Load dynamics are the driving force for voltage
instability [1].
b
Controlle
r
–  Tap changing transformers
Dynamic loads
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[1] P. Kundur, J. Paserba, V. Ajjarapu, G. Andersson, A. Bose, C. Canizares, N. Hatziargyriou, D. Hill, A. Stankovic, C. Taylor, T. Van Cutsem,
and V. Vittal, “Definition and classification of power system stability IEEE/CIGRE joint task force on stability terms and definitions,”
IEEE Transactions on Power Systems, no. 3, pp. 1387–140.
Dynamic stability criterion based
on static solutions
•  The system stability depends on:
–  Individual component stability, e.g. individual load
–  Connective stability
•  Under normal fixed voltage condition, the loads are
stable. Therefore, the connective stability determines the
system stability.
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Dynamic stability criterion based
on static solutions
•
U=const
Load
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Dynamic stability criterion based
on static solutions
•
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Dynamic stability criterion based
on static solutions
Load flow solutions:
Jacobian matrix:
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Dynamic stability criterion based
on static solutions
Each load is stable:
Let:
where then Lyapunov stability condition: the system is stable iff
there exists
s.t.
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Dynamic stability criterion based
on static solutions
(*)
Statement: if
then (*) is true with Stability criterion relies only on load flow solutions.
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Dynamic stability criterion based
on static solutions
•  Simulation results
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Trapped at the lower branch
•  Under typical scenarios such as when subjected to
disturbances or shedding loads, the system may be
trapped at a equilibrium on the lower branch without
violating any voltage constraints.
•  New policies for DGs should be introduced to prevent the
system gets stuck at the lower branch.
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Trapped at the lower branch
A 3-bus network case
•  Consider a 3-bus network having two dynamic loads based on the IEEE
Standard 4-Node Test Feeder [2].
P2= -1.095
P3= -0.984
Q2= -1.328
Q3= -1
tau1=tau2=100s
f1(|V|2)=f2(|V|2)=1
Voltage
Bus #2
Bus #3
1st solution (high
voltage)
1.080
1.200
2nd solution (low
voltage)
0.821
1.013
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[2]
IEEE PES Distribution System Analysis Subcommittee’s Distribution Test Feeder
Working Group, “Distribution test feeders.”
Trapped at the lower branch
•  Dynamic simulations: The nose curves at load bus #2 & #3
P3-V3
P3-V3
P2-V2
t=1000s
P3-V3
P2-V2
t=1500s
P3-V3
P2-V2
P2-V2
t=2000s
t=2060s
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Trapped at the lower branch
P3-V3
•  Dynamic simulations
P2-V2
P2-V2
t=3000s
t=100100s
Disturbance
Disturbance
Demand at bus #2 at t=2000s
Demand at bus #2 at t=100100s
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Trapped at the lower branch
A 2-bus network case with a transformer
•  Consider a 2-bus network a transformer to control the voltage at bus #2.
V1=1
V2
Line
R=0.072
X=0.258
P3= -2.327
Q3= 0.033
The transformer equation:
V3
K
y=const
Voltage
Bus #2
1st solution (high voltage)
0.940
2nd solution (low voltage)
0.667
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Trapped at the lower branch
A 2-bus network case with a transformer
•  Dynamic simulations: The nose curves at the load bus
P3-V2
Load shedding
Load impedance y(t)
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Trapped at the lower branch
A 2-bus network case with a transformer
•  Dynamic simulations: The nose curves at load bus
P3-V2
P3-V2
P2-V2
Load shedding
Load impedance y(t)
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Conclusions
•  The nose curve characteristics and the system stability can change
considerably due to power reversal and load dynamics.
•  The new stability criterion can be helpful in planning and
assessment of the system stability when the load dynamics are
unknown in advance.
•  Since low voltage solution may be stable, the system may be
trapped at the lower branch of the nose curve. In order to prevent
such situations, new policies such as to standardize power factors
or to regulate reactive power compensation should be introduced.
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Skoltech University
•  Graduate University built by
MIT outside of Moscow.
•  Energy Systems CREI:
–  Collaboration between
MIT, Caltech, LANL,
PNNL and others
–  Led by Janusz Bialek
–  Multiple faculty and
postdoctoral openings